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Updated: May 30, 2026
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Published on: July 21, 2018
Exact solutions for the source-excited cylindrical electromagnetic waves in a nonlinear nondispersive medium
V A Es'kin1, A V Kudrin, E Yu Petrov
1University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia.
Summary
Researchers solved the problem of nonlinear waves in curvilinear coordinates. This study presents the first exact solution for electromagnetic fields in inhomogeneous, nonlinear media excited by a pulsed current filament.
Area of Science:
- Electromagnetism and Photonics
- Nonlinear Optics
- Wave Propagation
Background:
- The study of electromagnetic fields in nonlinear media is a significant area of research.
- Finding exact solutions for source-excited nonlinear waves in curvilinear coordinates has been a long-standing challenge.
- Materials exhibiting nonlinear electromagnetic properties are crucial for advanced optical applications.
Purpose of the Study:
- To present the first exact solution for nonlinear electromagnetic waves in curvilinear coordinates.
- To investigate the behavior of cylindrically symmetric fields in inhomogeneous and nonlinear media.
- To analyze the properties of electromagnetic fields excited by a pulsed current filament.
Main Methods:
- Derivation of an exact solution for electromagnetic fields.
- Utilizing a medium with a power-law permittivity profile in the linear regime.
- Considering a medium that lacks a center of inversion.
- Analyzing a cylindrically symmetric field excited by a pulsed current filament.
Main Results:
- An exact solution for the electromagnetic field in a simultaneously inhomogeneous and nonlinear medium was derived.
- The solution pertains to a cylindrically symmetric field excited by a pulsed current filament.
- Properties of the derived exact solution were discussed, offering new insights into nonlinear wave behavior.
Conclusions:
- The study successfully provides the first exact solution for nonlinear waves in curvilinear coordinates.
- The findings open new avenues for understanding and manipulating electromagnetic fields in complex media.
- This work contributes to the theoretical framework of nonlinear electromagnetism and its applications.
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